Abstract
It is known that under certain mild set-theoretic assumptions, a finite, countably additive measure defined on all Borel sets of a metric space is concentrated in a separable subspace (Marczewski and Sikorski [8]). However, there are interesting probability measures on metric spaces not concentrated in separable subspaces. In this paper, we consider countably additive probability measures on the smallest σ-field containing the open balls of a metric space. This σ-field is the Borel field for a separable space, but is smaller in general. A probability measure on it need not be confined to a separable subspace.
Received September 28, 1964.
Partially supported by a national Science Foundation Grant and by the Office of Naval Research.
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Dudley, R.M. (2010). Weak Convergence of Probabilities on Nonseparable Metric Spaces and Empirical Measures on Euclidean Spaces. In: Giné, E., Koltchinskii, V., Norvaisa, R. (eds) Selected Works of R.M. Dudley. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5821-1_2
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DOI: https://doi.org/10.1007/978-1-4419-5821-1_2
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